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Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition

View Article: PubMed Central - PubMed

ABSTRACT

Epileptic absence seizure characterized by the typical 2–4 Hz spike-wave discharges (SWD) are known to arise due to the physiologically abnormal interactions within the thalamocortical network. By introducing a second inhibitory neuronal population in the cortical system, here we propose a modified thalamocortical field model to mathematically describe the occurrences and transitions of SWD under the mutual functions between cortex and thalamus, as well as the disinhibitory modulations of SWD mediated by the two different inhibitory interneuronal populations. We first show that stimulation can induce the recurrent seizures of SWD in the modified model. Also, we demonstrate the existence of various types of firing states including the SWD. Moreover, we can identify the bistable parametric regions where the SWD can be both induced and terminated by stimulation perturbations applied in the background resting state. Interestingly, in the absence of stimulation disinhibitory functions between the two different interneuronal populations can also both initiate and abate the SWD, which suggests that the mechanism of disinhibition is comparable to the effect of stimulation in initiating and terminating the epileptic SWD. Hopefully, the obtained results can provide theoretical evidences in exploring dynamical mechanism of epileptic seizures.

No MeSH data available.


Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.(a) The state transition diagram as the k8 varying in [1.3, 1.7] with k6 = 1.5, corresponding to the upward pink arrow in Fig. 13(a). The system transits from high saturated firing denoted by ‘I’ to clonic oscillations (II), SWD discharges (III), low saturated firing (IV) and to the simple tonic oscillation (V).
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f14: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.(a) The state transition diagram as the k8 varying in [1.3, 1.7] with k6 = 1.5, corresponding to the upward pink arrow in Fig. 13(a). The system transits from high saturated firing denoted by ‘I’ to clonic oscillations (II), SWD discharges (III), low saturated firing (IV) and to the simple tonic oscillation (V).

Mentions: Particularly, here we take k4 = 1 and k10 = 3, as shown in Fig. 5(a) which lies in the region of stimulus-induced SWD. And importantly, we can see from Figs 10 and 12, when the inhibitory regulating function of IN2 is larger than k6 = 1.05, the SWD discharges can be completely induced. Hence, in order to observe the disinhibition effect of IN1, k8, on the inhibition-induced SWD, we here consider a local parameter region of (k6, k8), [1.3, 1.7] × [1.3, 1.7], where the critical value of k6 is larger than k6 = 1.05, which can absolutely induce the occurrence of SWD discharge. As shown in Fig. 13(a), from the bottom to top, there are five different firing states including high saturated firing indicated by (I), simple clonic oscillation (II), periodic spike-wave discharge (SWD) (III), low saturated firing (IV) and the simple tonic oscillation (V). Accordingly, the variation of corresponding dominant frequency has been given in the Fig. 13(b), where regions ‘A’, ‘C’ and ‘D’ correspond to the regions ‘I’, ‘IV’ and ‘V’, respectively. Additionally, the similar firing frequency regions ‘II’ and ‘III’ are combined into the region ‘B’. We can see from Fig. 8(a) that the system is stable to the variation of k6 within [1.3, 1.7] with any fixed k8. However, as k8 is increased from 1.3 to 1.7, for any k6 ∈ [1.3, 1.7] the system can show rich dynamic transitions from high saturated firing to clonic oscillation, SWD discharges, low saturated firing, and to tonic oscillation. For a clearer vision, corresponding to the vertical pink arrow in the Fig. 13(a), Fig. 14 depicts the 1-D dynamic transition diagram with k6 = 1.5 and k8 varying in [1.3, 1.7]. Various firing state parameter intervals corresponding to different regions of ‘I’, ‘II’, ‘III’, ‘IV’ and ‘V’ can be found. As typical examples, we also take several parameter values of (k6, k8) from the vertical pink arrow in Fig. 13(a) corresponding to the different firing states in Fig. 14, to illustrate the various firings. Figure 15 shows the typical time series of the mean for the excitatory neuronal population, PY, and inhibitory neuronal populations, IN1. Particularly, as k6 = 1.5, we take k8 = 1.3, 1.4, 1.48, 1.55 and 1.7, respectively. And then, the system successively displays high saturated firing corresponding to the Fig. 15(a), clonic oscillation (Fig. 15(b)), periodic spike and slow-wave discharges (SWD) (Fig. 15(c)), low saturated firing (Fig. 15(d)) and tonic oscillation corresponding to the Fig. 15(e), respectively.


Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition
Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.(a) The state transition diagram as the k8 varying in [1.3, 1.7] with k6 = 1.5, corresponding to the upward pink arrow in Fig. 13(a). The system transits from high saturated firing denoted by ‘I’ to clonic oscillations (II), SWD discharges (III), low saturated firing (IV) and to the simple tonic oscillation (V).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5120301&req=5

f14: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.(a) The state transition diagram as the k8 varying in [1.3, 1.7] with k6 = 1.5, corresponding to the upward pink arrow in Fig. 13(a). The system transits from high saturated firing denoted by ‘I’ to clonic oscillations (II), SWD discharges (III), low saturated firing (IV) and to the simple tonic oscillation (V).
Mentions: Particularly, here we take k4 = 1 and k10 = 3, as shown in Fig. 5(a) which lies in the region of stimulus-induced SWD. And importantly, we can see from Figs 10 and 12, when the inhibitory regulating function of IN2 is larger than k6 = 1.05, the SWD discharges can be completely induced. Hence, in order to observe the disinhibition effect of IN1, k8, on the inhibition-induced SWD, we here consider a local parameter region of (k6, k8), [1.3, 1.7] × [1.3, 1.7], where the critical value of k6 is larger than k6 = 1.05, which can absolutely induce the occurrence of SWD discharge. As shown in Fig. 13(a), from the bottom to top, there are five different firing states including high saturated firing indicated by (I), simple clonic oscillation (II), periodic spike-wave discharge (SWD) (III), low saturated firing (IV) and the simple tonic oscillation (V). Accordingly, the variation of corresponding dominant frequency has been given in the Fig. 13(b), where regions ‘A’, ‘C’ and ‘D’ correspond to the regions ‘I’, ‘IV’ and ‘V’, respectively. Additionally, the similar firing frequency regions ‘II’ and ‘III’ are combined into the region ‘B’. We can see from Fig. 8(a) that the system is stable to the variation of k6 within [1.3, 1.7] with any fixed k8. However, as k8 is increased from 1.3 to 1.7, for any k6 ∈ [1.3, 1.7] the system can show rich dynamic transitions from high saturated firing to clonic oscillation, SWD discharges, low saturated firing, and to tonic oscillation. For a clearer vision, corresponding to the vertical pink arrow in the Fig. 13(a), Fig. 14 depicts the 1-D dynamic transition diagram with k6 = 1.5 and k8 varying in [1.3, 1.7]. Various firing state parameter intervals corresponding to different regions of ‘I’, ‘II’, ‘III’, ‘IV’ and ‘V’ can be found. As typical examples, we also take several parameter values of (k6, k8) from the vertical pink arrow in Fig. 13(a) corresponding to the different firing states in Fig. 14, to illustrate the various firings. Figure 15 shows the typical time series of the mean for the excitatory neuronal population, PY, and inhibitory neuronal populations, IN1. Particularly, as k6 = 1.5, we take k8 = 1.3, 1.4, 1.48, 1.55 and 1.7, respectively. And then, the system successively displays high saturated firing corresponding to the Fig. 15(a), clonic oscillation (Fig. 15(b)), periodic spike and slow-wave discharges (SWD) (Fig. 15(c)), low saturated firing (Fig. 15(d)) and tonic oscillation corresponding to the Fig. 15(e), respectively.

View Article: PubMed Central - PubMed

ABSTRACT

Epileptic absence seizure characterized by the typical 2–4 Hz spike-wave discharges (SWD) are known to arise due to the physiologically abnormal interactions within the thalamocortical network. By introducing a second inhibitory neuronal population in the cortical system, here we propose a modified thalamocortical field model to mathematically describe the occurrences and transitions of SWD under the mutual functions between cortex and thalamus, as well as the disinhibitory modulations of SWD mediated by the two different inhibitory interneuronal populations. We first show that stimulation can induce the recurrent seizures of SWD in the modified model. Also, we demonstrate the existence of various types of firing states including the SWD. Moreover, we can identify the bistable parametric regions where the SWD can be both induced and terminated by stimulation perturbations applied in the background resting state. Interestingly, in the absence of stimulation disinhibitory functions between the two different interneuronal populations can also both initiate and abate the SWD, which suggests that the mechanism of disinhibition is comparable to the effect of stimulation in initiating and terminating the epileptic SWD. Hopefully, the obtained results can provide theoretical evidences in exploring dynamical mechanism of epileptic seizures.

No MeSH data available.